Potential at a Distance away from a FINITE continuously charged plane

In summary, the conversation is about a programming question on finding the potential at a specific distance from the center of a square plane using the equation V = integral (k/r) dq. The proposed solution involves a two integral method and substituting lambda for sigma in order to account for even charge distribution. The person is seeking advice on the method and setup of the integration. Reference material is also mentioned.
  • #1
BeRiemann
15
0

Homework Statement


This is primarily a question that I'm trying to program into python. I want to know the potential at some distance (x,y) from the center of a square plane.


Homework Equations


V = integral (k/r) dq


The Attempt at a Solution


The way I see this mathematically is a two integral method. First I figure out the potential from a finite line with a continuous charge. This can be seen as dx or dy, such as the next step integrates this over either the width or length of the plane. If the point had no shift in x, it could be imagined as a pyramid.
I have the line charge done, though it is in terms of lambda = Q/L, when I actually have a sigma = Q/A. With an even charge distribution, I should be able to substitute (Q/(Length*width)) for lambda as long as I use it in both integrals.

Again, just looking for some advice into the method or the setup of the integration. I can take it from there in terms of the programming or simplifying.
 
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  • #2
As a reference I'm trying to do this
http://www.physics.upenn.edu/courses/gladney/phys151/lectures/lecture_jan_17_2003.shtml#tth_sEc1.3.3 [Broken]
but with electric potential in a general form.
 
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1. What is the definition of "Potential at a Distance away from a FINITE continuously charged plane"?

The potential at a distance from a finite continuously charged plane is the amount of electrical potential energy per unit charge at that specific distance from the plane.

2. How is the potential at a distance away from a finite continuously charged plane calculated?

The potential at a distance away from a finite continuously charged plane can be calculated using the formula V = kσ/2ε0, where V is the potential, k is the Coulomb's constant, σ is the surface charge density of the plane, and ε0 is the permittivity of free space.

3. What factors affect the potential at a distance away from a finite continuously charged plane?

The potential at a distance away from a finite continuously charged plane is affected by the magnitude of the charge on the plane, the distance from the plane, and the surface charge density of the plane.

4. How does the potential at a distance away from a finite continuously charged plane change with distance?

The potential at a distance away from a finite continuously charged plane follows an inverse relationship with distance. As the distance from the plane increases, the potential decreases.

5. Can the potential at a distance away from a finite continuously charged plane ever be negative?

Yes, the potential at a distance away from a finite continuously charged plane can be negative. This occurs when the charge on the plane is negative and the distance from the plane is large enough for the potential to become negative.

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